Mask Pattern Arrangement Using Discretized Intensity Functions
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Solution Overview
Problem
Current methods for arranging mask patterns in semiconductor fabrication fail to efficiently determine the position of additional patterns to optimize image intensity and exposure on semiconductor wafers, leading to suboptimal performance in integrated circuit fabrication.
Innovation Solution
The method involves obtaining a distribution of functions representing the contribution of a second pattern to image intensity, discretizing neighboring regions into finite regions, and determining the position of the second pattern using polygonal regions with representative values, which enhances image intensity and exposure by applying optical proximity correction and mask rule checks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If current methods for arranging mask patterns are used, then the process is simple, but the speed of determining pattern position is slow and image intensity optimization is insufficient
Solution Approach 1:
The patent segments the continuous function distribution h(ξ−x) into discrete representative values h(x,ξ) at specific polygonal regions. This segmentation allows faster computation by replacing continuous function evaluation with discrete value lookup, directly improving the speed of determining pattern position while maintaining acceptable accuracy for optimization purposes.
Solution Approach 2:
The patent changes the representation parameter from continuous function distribution to discrete representative values at polygonal regions. This parameter change transforms the computational problem from evaluating continuous functions to comparing discrete values, significantly accelerating the pattern position determination process.
2Loss of time
If continuous function distribution is used, then accuracy is high, but computation time is excessive
Solution Approach 1:
By segmenting the function distribution into discrete representative values at polygonal regions, the patent reduces computation time from evaluating continuous functions to comparing discrete values, while maintaining sufficient precision for determining optimal pattern positions that maximize image intensity.
Solution Approach 2:
The patent uses representative values at specific polygonal regions rather than evaluating the function everywhere. This partial action approach provides sufficient precision for optimization purposes without the excessive computation time required for complete continuous function evaluation.
3Illumination intensity
If more patterns are added to optimize image intensity, then exposure performance improves, but determining the position becomes more complex
Solution Approach 1:
The patent applies local quality by using representative values h(x,ξ) at specific polygonal regions around each pattern. This allows efficient determination of second pattern positions that optimize image intensity at local regions, enabling multiple patterns to be arranged with improved exposure performance without excessive computational complexity.
Solution Approach 2:
By changing from continuous function evaluation to discrete representative value comparison, the patent enables complex multi-pattern arrangements to be optimized efficiently. The parameter change allows the system to handle multiple patterns while keeping the position determination process computationally manageable.
Data Source
AI summary
Methods and apparatus are disclosed that arrange mask patterns in response to the contribution of a second pattern to image intensity. In some methods of arranging mask patterns, a distribution of functions h(ξ−x) is obtained which represents the contribution of a second pattern to image intensity on a first pattern. Neighboring regions of the first pattern are discretized into finite regions, and the distribution of the functions h(ξ−x) is replaced with representative values h(x,ξ) of the discretized regions. A position of the second pattern is determined using polygonal regions having the same h(x,ξ). As described, the term x is the position of the first pattern and the term ξ is the position of the assist.